peperiksaan percubaan sijil pelajaran malaysia 2007spm\pahang\addmaths\2007\th…sijil pelajaran...

$: PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2007SPM\Pahang\AddMaths\2007\Th…SIJIL PELAJARAN MALAYSIA 2007 ADDITIONAL MATHEMATICS Paper 1 2 hours JANGAN BUKA KERTAS SOALAN INI$
SULIT 3472/1

3472/1 SULIT

NO.KAD PENGENALAN/I.C NUMBER- -

ANGKA GILIRAN/INDEX NUMBER

_________________________________

PEPERIKSAAN PERCUBAANSIJIL PELAJARAN MALAYSIA 2007

ADDITIONAL MATHEMATICSPaper 12 hours

JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

1. Tuliskan angka giliran dan nombor kadpengenalan anda pada ruang yangdisediakan.

Write your index number and I.C.number in the space provided.

2. Calon dikehendaki membaca arahan dihalaman 2 dan halaman 3

Candidates are required to read theintructions on page 2 and 3

____________________________________________________________________________________________________________________________________________________

Kertas soalan ini mengandungi 20 halaman bercetak.

Examiner’s CodeQuestion Full Marks

Marks Acquired1 22 43 34 35 46 37 48 49 310 311 212 413 314 315 316 417 318 219 320 321 422 323 424 325 3

Total 80

3472/1Form FiveAdditional MathematicsPaper 1September 20072 hours Nama Calon :

Tingkatan :

TheMind's Q'Bank - A non-profit community initiative by TheMind Association www.themindassociation.org

TheMind's Q'Bank Note - The Intellectual Property of the question set lies with its original copyright owner.Use the document as a complete set and do not ammend any pages.

SULIT 3472/1

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MAKLUMAT UNTUK CALON

1. Kertas soalan ini mengandungi 25 soalan.

2. Jawab semua soalan.

3. Bagi setiap soalan berikan SATU jawapan sahaja.

4. Jawapan hendaklah ditulis dengan jelas dalam ruang yang disediakan dalam kertas

soalan.

5. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu

anda untuk mendapatkan markah.

6. Sekiranya anda hendak menukarkan jawapan, batalkan kerja mengira yang telah

dibuat. Kemudian tuliskan jawapan yang baru.

7. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyatakan.

8. Markah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan

dalam kurungan.

9. Satu senarai rumus disediakan di halaman 4 hingga 6.

10. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

11. Kertas soalan ini hendaklah diserahkan di akhir peperiksaan.



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INFORMATION FOR CANDIDATES

1. This question paper consists of 25 questions.

2. Answer ALL questions.

3. Give only ONE answer for each question.

4. Write your answer clearly in the spaces provided in the question paper.

5. Show your working. It may help you to get marks.

6. If you wish to change your answer, cross out the work that you have done. Then write

down the new answer.

7. The diagram in the questions provided are not drawn to scale unless stated.

8. The marks allocated for each question and sub-part of a question are shown in

brackets.

9. A list of formulae is provided on pages 4 to 6.

10. You may use a non-programmable scientific calculator.

11. This question paper must be handed in at the end of the examination.



SULIT 3472/1

[See overleaf3472/1 SULIT

5

ALGEBRA

1a

acbbx2

42 8ab

bc

ca log

loglog

2 am x an = a m + n 9 Tn = a + (n -1)d

3 am an = a m – n 10 Sn = 2 ( 1)2n a n d

4 ( am )n = a m n 11 Tn = 1nar

5 nmmn aaa logloglog 12 ( 1) (1 ) , 11 1

n n

na r a rS r

r r

6 nmnm

aaa logloglog 13 , 11

aS rr

7 log a mn = n log a m

CALCULUS

1dxduv

dxdvu

dxdyuvy ,

4 Area under a curve=b

a

y dx orb

a

x dy2 2,

vdxdvu

dxduv

dxdy

vu

y

3dxdu

dudy

dxdy

5 Volume generated

= 2b

a

y dx or

= 2b

a

x dy



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6

STATISTICS

1Nxx 8 !

( )!n

rn

Pn r

2ffxx

9 !

( )! !n

rn

Cn r r

3 2

22

xNx

Nxx

10 ( ) ( ) ( ) ( )P A B P A P B P A B

4 2

22

xf

fxf

xxf

11 P(X = r) = , 1n r n rrC p q p q

5 Cf

FNLm

m

2

1

12 Mean = np

6 1

0100QI

Q

13 npq

7i

ii

WIW

I

14 XZ

GEOMETRY

1 Distance = 2 22 1 2 1( ) ( )x x y y

4 Area of a triangle =

12 1 2 2 3 3 1 2 1 3 2 1 3( ) ( )x y x y x y x y x y x y

2 Midpoint =

2,

22121 yyxx

5. 22

~yxr

3 A point dividing a segment of a line(x , y ) =

nmmyny

nmmxnx 2121 ,

622

~~

~

^

yx

jyixr



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7

TRIGONOMETRY

1 Arc length, s =r 8 sin( ) sin cos cos sinA B A B A B

2 Area of a sector, 212

A r 9 cos( ) cos cos sin sinA B A B A B

3 . 2 2sin cos 1A A 10 tan tantan( )

1 tan tanA B

A BA B

4 2 2sec 1 tanA A11 2

2 tantan 2

1 tanA

AA

5 2 2cos 1 cotec A A 12sin sin sin

a b cA B C

6 sin 2A = 2 sin A cos A 13 2 2 2 2 cosa b c bc A

7 cos 2A = 2 2cos sinA A= 22cos 1A= 21 2sin A

14 Area of triangle = 1 sin2

ab C



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Answer all questions.

1 Based on the above information, the relation between M and N is defined by the set

of ordered pairs { (-2, 1 ), (-1, 0 ), ( 0, 1 ), ( 1, 2 ), (2, 3 )}.

State

(a) the image of 2.(b) the object of 0.

[2 marks]

Answer : (a)…………………………………

(b)…………………………………

2 Given that f : x 3x – 4 and g : x x 2 +8 x + 16, find

(a) f -1 ( 5 )(b) g f ( x )

[4 marks]

Answer : (a)…………………………………

(b)…………………………………

M ={ -3, -2, -1, 0, 1, 2 }

N ={ -1, 0, 1, 2, 3 }

2

1

4

2



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9

3 -3 is one of the roots of the quadratic equation 2 x2 + p x =3

Find

( a ) the value of p

( b ) the value of the other root.

[3 marks]

Answer : (a)…………………………………

(b)…………………………………

4. The quadratic equation ( 2 x – 5 )2 = (p – 10) x has two distinct roots.

Find the range of values of p.

[3 marks]

Answer : …………………………………

3

3

3

4



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5. Solve 3 3log (4 ) log ( 1) 1x x [4 marks]

Answer : …………………………………

6. Solve the equation 3 2x .[3 marks]

Answer : …………………………………

4

5

3

6



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11

7. During the year 2005, a company increased its sales of digital cameras at a constantrate of 200 units per month. Thus the number of digital cameras sold in Februarywas 200 more than in January, the number of digital cameras sold in March was 200more than in February, and this pattern continued month by month throughout theyear. Given that the company sold 38,400 units of digital cameras in the year 2005.

Calculate the number of units of digital cameras sold in

(a) January 2005

(b) December 2005[4 marks]

Answer : (a)…………………………………

(b)…………………………………

8. The first three terms of a geometric progression are x+10, x-2 and x-10 respectively.Calculate

(a) the value of x.

(b) the sum to infinity of this progression.[4 marks]

Answer : (a)…………………………………

(b)…………………………………

4

7

4

8



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9. A point P (8, t ) divides the line joining A (4, 1) and B ( r , 7 ) such that3AP = 2PB. Find the value of

(a) r

(b) t[3 marks]

Answer : (a)…………………………………

(b)…………………………………

10. The straight lines y = mx + 9, where m is a constant, and 2y = x 2 areperpendicular.

(a) Find the value of m,

(b) Hence or otherwise, find the coordinates of the point of intersection of thelines.

[3 marks]

Answer : (a)…………………………………

(b)…………………………………

3

9

3

10



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13

11 Diagram 1 shows vectors CB

and BA

. A, B and C are ( 0, h ), ( 5, 3 ) and ( 2, 7 )respectively.

DIAGRAM 1

(a) Express CB

in the form of xi yj

(b) Given that 5 7BA i j

, find the corresponding value of h.

[2 marks]

Answer : (a)…………………………………

(b)… ………………………………

2

11

O



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12 Diagram 2 shows a parallelogram ABCD with BED as a straight line.

Given that 5AB

p, BC

= 3q, and 4DE = EB. Express in terms of p and q :

(a) BD

(b) EC

[4 marks]

Answer : (a)…………………………………

(b)… ………………………………

A

B

C

D

E

DIAGRAM 2

4

12



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13. Given that 2 2a i j

, 2 3b i j

and 2c a b

. Find

(a) c

(b) unit vector in the direction of c

.[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

14. The net value, m in hundreds of ringgit, of the monthly output of a factory is

modelled by2 3

10 3000n n

m where n is the number of working hours a worker put

in per month. Calculate the value of n such that m is maximum.[3 marks]

Answer : n =…………………………………

3

14

3

13



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15 The radius of a spherical balloon is increasing at the rate of x cms-1.Given that the rate of change of the volume of the balloon is 25cm3 s -1 when

its radius is 5 cm. Find the value of x. [ 343

V r ]

[3 marks]

Answer : …………………………………

16 x and y are related by the equationm

x nyx

, where m and n are constants.

A straight line is obtained by plotting xy against x2, as shown in Diagram 3.

Calculate the value of m and of n.[4 marks]

Answer : m=…………………………………

n=…………………………………

xy

(12, 2 )

( 6, 0) x 2

DIAGRAM 3

4

16

3

15



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17 Given that5

1

( ) 5g x dx , find the value of m if

5

1

[ 2 ( )] 3mx g x dx m [3 marks]

Answer : …………………………………

18 Diagram 4 shows the quadratic curve y = g(x) and the line PQ. PQ is parallel to thex-axis.

Given that the curve has a minimum value at O, the origin, the curve

intersects line PQ at R (b, 4). Given that the area of the shaded region is13

.

Find 2 ( )b

b

g x dx

[2 marks]

Answer : …………………………………

2

18

3

17

P Q

O

y

x

y = g(x)

DIAGRAM 4

R(b,4)



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19 A circle of radius 2.5 cm has a minor sector with an area of 6.25 cm2. Calculate

( a ) the angle of the sector in radians,

( b ) the perimeter of the major sector.

[ use 3.142 ][3 marks]

Answer : (a)…………………………………

(b)… ………………………………

20 Given that x is an acute angle and sinm

xn

, find 1+ tan(90 )x in terms of

m and n.[3 marks]

Answer : …………………………………

3

20

3

19



SULIT 3472/1


19

21 Solve 3cos 2x + 4 cos x +1 = 0 for 0 360x

[4 marks]

Answer : …………………………………

22 An expedition team consisting of 10 members to be chosen from a group of 4teachers and 12 students.

(a) Calculate the number of teams that can be formed.

(b) If the team must consist of at least 2 teachers, calculate the numbers of teamsthat could be formed.

[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

3

22

4

21



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23 (a) How many possible arrangements in a row, can all the letters from the word“ C E R I A “ be arranged ?

(b) An arrangement in (a) is chosen at random, find the probability that thearrangement will have both ‘A’ and ‘E ‘ separated.

[4 marks]

Answer : (a)…………………………………

(b)… ………………………………

24 Diagram 5 shows a standard normal distribution graph.

The probability represented by the area of the shaded region is 0.803.

(a) Find the value of P( Z > k )

(b) X is a continuous random variable which is normally distributed with a mean ofand a standard deviation of 2. If the value of X is 85 when the Z-score is k,find the value of .

[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

-k k z

f(z))

0.803

DIAGRAM 5

3

24

4

23



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25 In a survey, the probability that a family owning one unit of computer is 0.6.N families were selected at random. The standard deviation of the numbers offamily owning one unit of computer is 1.697.

Find(a) the value of N(b) the mean of the numbers of family owning one unit of computer.

[3 marks]

Answer : (a)…………………………………

(b)… ………………………………

END OF QUESTION PAPER

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